"The LLL algorithm"

In this talk we are going to explain the LLL algorithm in a conceptual manner. We start by doing the analysis of Gauss's reduction procedure for rank 2 lattices. From this we describe LLL as a family of algorithms that given an arbitrary basis of a lattice calculates a "c-reduced" basis for this lattice by successive application of rank 2 reduction. Attention will be given to the properties of this basis and we conclude with some applications.